Should the saddle be higher than the handlebars?
In many cases, cyclist who race will most of the time have saddle higher than handlebar, but it is a very individual thing and it should be customized for everyone separately. We recommend start you cycling journey with a proper bike fitting by professional. Many time you can do it in local bike shop.
It depends how you ride a bike. If the rider is racing, then s/he wants the bars lower than the saddle to provide an aerodynamic position. But if the rider is a recreational cyclist, then s/he will want the bars higher than the saddle for a more upright position that is more comfortable— easier on the neck— and allows for greater visibility.
Your saddle height must be set for proper leg extension while pedalling. The height of your bars has no relevance to your saddle height. The way you worded your post made me think you are adjusting the saddle to determine the height difference between the saddle and bars, but you adjust your saddle to the correct height and then decide where the bars go.
I think most racers would prefer the saddle higher than the handlebars, but if you think you race better the other way around that’s fine too.
Definitely up to personal preference. For me my saddle is higher than the bars.